Proving termination of evaluation for System F with control operators Małgorzata Biernacka Dariusz Biernacki Sergue¨ıLenglet Institute of Computer Science Institute of Computer Science LORIA University of Wrocław University of Wrocław Universit´ede Lorraine
[email protected] [email protected] [email protected] Marek Materzok Institute of Computer Science University of Wrocław
[email protected] We present new proofs of termination of evaluation in reduction semantics (i.e., a small-step opera- tional semantics with explicit representation of evaluation contexts) for System F with control oper- ators. We introduce a modified version of Girard’s proof method based on reducibility candidates, where the reducibility predicates are defined on values and on evaluation contexts as prescribed by the reduction semantics format. We address both abortive control operators (callcc) and delimited- control operators (shift and reset) for which we introduce novel polymorphic type systems, and we consider both the call-by-value and call-by-name evaluation strategies. 1 Introduction Termination of reductions is one of the crucial properties of typed λ-calculi. When considering a λ- calculus as a deterministic programming language, one is usually interested in termination of reductions according to a given evaluation strategy, such as call by value or call by name, rather than in more general normalization properties. A convenient format to specify such strategies is reduction semantics, i.e., a form of operational semantics with explicit representation of evaluation (reduction) contexts [14], where the evaluation contexts represent continuations [10]. Reduction semantics is particularly convenient for expressing non-local control effects and has been most successfully used to express the semantics of control operators such as callcc [14], or shift and reset [5].